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0580/33 Oct/Nov 2024, Question 9: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Using shapes A, B and C on a coordinate grid, identify shape A, describe transformations mapping A to B and A to C, and draw images of A after a 90° clockwise rotation about (0, 0) and a reflection in x = 1.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

State the mathematical name of shape A from the grid.

  1. 1One pair of parallel sides: trapezium

AnswerTrapezium

Part (b) · 3 marks

Describe fully the single transformation taking shape A onto shape B.

  1. 1Lengths halve: base 5 − 3 = 2 becomes 3.5 − 2.5 = 1, so scale factor 0.5
  2. 2Join (3, 3) to (2.5, 2) and (5, 3) to (3.5, 2) and extend: they meet at (2, 1)
  3. 3Enlargement, scale factor 0.5, centre (2, 1)

AnswerEnlargement, scale factor 0.5, centre (2, 1)

Part (c) · 2 marks

Describe fully the single transformation taking shape A onto shape C.

  1. 1Match a corner: (3, 3) on A goes to (−4, −2) on C.
  2. 2Across: −4 − 3 = −7
  3. 3Up: −2 − 3 = −5
  4. 4Translation, column vector (−7, −5)

AnswerTranslation, column vector (−7, −5)

Part (d) · 2 marks

Draw shape A's image after a 90° clockwise rotation about centre (0, 0).

  1. 1(x, y) → (y, −x)
  2. 2(3, 3) → (3, −3), (3, 4) → (4, −3), (4, 4) → (4, −4), (5, 3) → (3, −5)
  3. 3Draw the shape with vertices (3, −3), (3, −5), (4, −3), (4, −4)

AnswerCorrect rotation, vertices at (3, −3) (3, −5) (4, −3) (4, −4)

Part (e) · 2 marks

Draw shape A's image after reflection in the line x = 1.

  1. 1(x, y) → (2 − x, y)
  2. 2(3, 3) → (−1, 3), (3, 4) → (−1, 4), (4, 4) → (−2, 4), (5, 3) → (−3, 3)
  3. 3Draw the shape with vertices (−3, 3), (−2, 4), (−1, 4), (−1, 3)

AnswerCorrect reflection, vertices at (−3, 3) (−2, 4) (−1, 4) (−1, 3)

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Also searched as: 0580/33/O/N/24 · 0580_w24_qp_33 · 0580 w24 33 · question 9.
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